If your talking about Far Cry 1 (WineHQ AppDB page)...
Then have you tried using the OpenGL renderer vs. the default DirectX renderer?
This would be preferable, performance and compatibility wise, since there would only be direct graphics call translations taking place.

Your problem is probably due to trying to use the Open Source Nouveau graphics driver.

I noticed that the game does load the first map, but after about 2 minutes. But considering that my iMac hardware meets the game's requirements and that I didn't have a problem when I ran the game through macOS Wineskin, this should not be happening.

Katakis wrote:I noticed that the game does load the first map, but after about 2 minutes. But considering that my iMac hardware meets the game's requirements and that I didn't have a problem when I ran the game through macOS Wineskin, this should not be happening.

That Mesa version is positively archaic... You'll want to update this to Mesa version ≥18.2.x

If the game still doesn't run, then you'll probably want to try the proprietary Nvidia Driver.
This is probably recommended anyway, as the Nouveau driver is severely hampered by Nvidia's total lack of support for it (e.g. it doesn't even support re-clocking for these cards at present - I believe).

There is an OpenGL renderer that has most of the visual effects present in the Direct3D one, but should run faster. To enable it, change "r_Driver" from "Direct3D9" to "OpenGL" in the 'system.cfg' file.